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The interpretation of droplet coalescence data using the log normal distribution

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Summary

The rest times of hydrocarbon oil droplets have been measured at the oil/sodium dodecyl sulphate solution interface. The existing equations, both physically derived and empirical, have been applied to the data obtained. In most cases the expressions used were not suitable for general application to our data.

From a consideration of the distribution of droplet rest times about the mean we conclude that the lognormal distribution would be the most suitable. The graphical test of this distribution function gave a good fit in each case. The method is useful in the analysis of stability data; results for each system can be characterized by the two parametersM and σg.

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Abbreviations

a :

coalescence constant, eq. [1]

F :

fraction of droplets coalesced at timet

k :

rate constant for coalescence

K :

coalescence constant, equation [3]

M :

geometric mean rest time=t1/2

n :

index

N :

number of drops remaining at timet

N 0 :

total number of drops observed

t :

time (seconds)

t 0 :

minimum rest time, eq. [3] and [4]

t d :

time required for film drainage

T 1/2:

first order half life for coalescence

t 1/2:

time required for half of droplets to coalesce

t :

max maximum rest time

t :

mean mean rest time

t :

min minimum rest time

x :

parameter log-normally distributed

y :

frequency function, eq. [8]

α :

coalescence constant eq. [2]

σ g :

geometric standard deviation

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Author notes

  1. S. S. Davis & A. Smith

    Present address: Pharmaceutics Research Group, University of Aston in Birmingham, Gosta Green, Birmingham 4, England

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    1. S. S. Davis
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    2. A. Smith
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    Davis, S.S., Smith, A. The interpretation of droplet coalescence data using the log normal distribution. Kolloid-Z.u.Z.Polymere 251, 337–342 (1973). https://doi.org/10.1007/BF01498732

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    • DOI: https://doi.org/10.1007/BF01498732

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